Question: Multiply.
$35 \times 21$ and $3.5 \times 0.21$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $35 \times 21$. Then we can estimate to place the decimal point in the product of $3.5 \times 0.21$. $\begin{aligned} 35&\\ \underline{ \times 21}&\\ 5}\\ 30}\\ 100}\\ \underline{+600}}\\ 735 \end{aligned}$ Let's estimate to place the decimal in $3.5 \times 0.21$. $\begin{aligned} 3.5 \times 0.21 &\approx 4 \times 0.2\\\\ &\approx \dfrac{4}{1}\times \dfrac{2}{10}\\\\ &\approx \dfrac{8}{10}\\\\ &\approx 0.8 \end{aligned}$ Where can we place the decimal in $735$ to get a product close to $0.8$ ? $0.735 = 3.5 \times 0.21$